Speech Transcript - COMPRESSIVE SENSING FOR OVER-THE-AIR ULTRASOUND

0:00:13	oh
0:00:14	oh
0:00:14	oh
0:00:15	they
0:00:30	yeah
0:00:31	so what i'd like to talk about the day is uh
0:00:34	an application that uh we've recently
0:00:37	um had the chance to apply compressed sensing and i think it's a very exciting application a little
0:00:42	a i apply applied this thing to ultrasound sound it's
0:00:45	go over the ultrasound sound ultrasonic sensing
0:00:48	i think it has a lot of implications for active sensing and wideband the raise and various
0:00:52	a as so
0:00:54	i'll start by setting up the problem
0:00:56	um the general idea is that we have an R a and that
0:00:59	the are a configuration is not something that
0:01:02	wherein in we we
0:01:03	are looking into right now
0:01:05	uh but we have a general or a and we have a scene
0:01:07	and not would like to do is illuminate the scene and a that scene
0:01:11	um
0:01:11	and we wanna do that as ultrasound and what would like to get
0:01:15	is would like to get the three D reflectivity of the
0:01:18	now this is not very easy
0:01:20	uh that's why we're trying to use a band of sound
0:01:24	um
0:01:25	and also what we wanna do is you wanna use a lot of the ideas from compressed sensing
0:01:29	now what makes us think that we can do that is that
0:01:33	every every object in the scene will reflect the old sound but the older sound doesn't penetrate up the object
0:01:37	so and i think behind that the object
0:01:40	we cannot see so we will appear zero in or
0:01:43	in our representation
0:01:45	if the object reflects the older sound it means that there was nothing in front of it to clothing it's
0:01:49	so everything in front of the object to zero
0:01:51	so if we describe is the same let's say by in in three dimensions and one and two and three
0:01:57	the number of points in the discrete a station
0:01:59	this scene has at most
0:02:01	uh
0:02:02	and and two times and one points to generally sparse use it's gonna be even sparse there
0:02:07	so that makes us uh be hopeful that a processing will work on that C
0:02:12	so
0:02:13	and it's try to see if we can model this the this whole system and see what we can do
0:02:17	with that
0:02:18	and then see if that helps as designed the sensing system and
0:02:21	a a how to get some reconstruction from that
0:02:24	so we'll start with by looking at the single transmitter and a single receiver
0:02:28	um in most of this
0:02:30	uh talk the transmitters are gonna be blue dots and the receivers
0:02:34	green little triangles
0:02:36	uh and then i'm gonna be talking about this it's
0:02:38	a simple a a a a single scene point
0:02:41	with something to in that
0:02:42	uh a um
0:02:44	i i'm gonna call seen point and
0:02:46	and the scene point can think of them as a a whole scene it's a three D scene
0:02:50	uh you can think of it as a whole vector
0:02:52	that goes from zero to the total number of points and you can that you just like rise the whole
0:02:56	three D volume
0:02:57	um
0:02:58	and the transmitter from that particular scene point has a certain distance
0:03:02	uh here here it's the S and and if you can see that they just realise they're bit
0:03:06	small
0:03:07	um and the receiver has another then so we can we can look at how long it takes the the
0:03:12	path for that particular using the speed of sound we can
0:03:15	calculate the the distance from transmitter to receiver
0:03:18	and see what's the phase delay given a set than oh also the set frequency and if we have a
0:03:23	wide don't also can always
0:03:25	uh take the for a transfer of that and look at
0:03:27	other propagation delay for um for for that particular point
0:03:32	so if we look at all the points every point has a particular propagation
0:03:36	a delay and if that the transmitter transmits a set a certain impulse
0:03:40	um this possible will go get reflected from a point
0:03:43	and and get see that the receiver
0:03:46	and therefore we can for every point that has that the reflectivity in the scene
0:03:50	uh we can write the propagation
0:03:52	which we can then put it
0:03:54	you know convert it to a matrix form
0:03:56	um for all the points in the scene so
0:03:59	in general will have a a
0:04:01	which is the for every C where it will be
0:04:04	and just realise or too small so for every receiver or the frequency spectrum that it will receive
0:04:09	we'll just put them all one on on the bottom of the other
0:04:12	and the the a matrix captures the pulses that we transmit in the frequency domain and how
0:04:17	the they get uh delayed to propagate for every every single point in that
0:04:21	and finds and times and in that big you
0:04:25	and then the signal the the signal that we're interested in is that reflectivity at which as we said before
0:04:30	it's bar
0:04:31	so the signal will be high if that point is or like i if there is something at that point
0:04:36	a zero otherwise
0:04:38	so overall well
0:04:40	we get a
0:04:42	we get something very from at right
0:04:44	you've seen that before
0:04:45	it's
0:04:46	now you can see
0:04:48	uh so we have received a the does i think matrix which is determined
0:04:52	by the pulse is that we put in every transmitter and the pulse say
0:04:55	and then a scene which we hope is sparse and we think it's sparse
0:05:00	now
0:05:01	have said that that's a model of the system what can we do to get do the acquisition what can
0:05:05	you do to recover
0:05:07	um the signal and and how can we how can work with is
0:05:11	um um
0:05:12	so
0:05:13	we know from compressed sensing that in order to do
0:05:16	to do that
0:05:18	that
0:05:19	matrix S to have something quick here's robert this some they various it is some kind of a right B
0:05:24	you you can there some or this
0:05:26	um
0:05:28	and
0:05:29	what we have to control this matrix is the pulses that the transmit from its it's transmitter so it's transmitter
0:05:34	we design a pulse that are gonna put and and then transmit that
0:05:38	um and there are a cover in it you know there are the the limits set we have some from
0:05:42	compressed sensing the a a typical K log and the we and so on
0:05:45	uh i'm i'm not gonna go do that
0:05:48	uh the point is that we want to make that matrix very dave verse some very kind of our i
0:05:52	P like
0:05:54	so
0:05:55	well what the sell what helped single processing randomisation
0:05:58	what we're gonna do is we're gonna take pulses
0:06:01	that are around and every transmitter all transmitters will transmit at the same time
0:06:05	and every transmitter will transmit around "'em" pulse
0:06:09	different pulse for transmitter
0:06:11	what that will do is that possible get reflected then get acquired by the receiver again with it in frequency
0:06:17	and then in this the sensing matrix what the what this allows us to do is have very low coherence
0:06:22	some very
0:06:22	a very good results
0:06:24	a a very good very good um so probability S S L you can think of it
0:06:28	um
0:06:29	i in the classical sense
0:06:30	you know that the
0:06:32	you you can't even sometimes in in very simple systems and you can do matched filtering and because the pulses
0:06:37	that sorry "'cause" your and you can
0:06:38	separate them
0:06:39	um
0:06:40	and now there are certain your marks said that like to make
0:06:43	oh generally the pulse oh
0:06:45	the the more
0:06:46	dft coefficients you can choose in that paul so if you think of the pulse and time domain taking the
0:06:51	frequency domain you have
0:06:53	you dft each answer them more
0:06:54	dft coefficients you can
0:06:56	to for that false and the better chances of recover you have
0:07:00	um um also the more transmitters and receivers you have a bigger matrix and you have a
0:07:05	uh a better chance of recovery
0:07:07	and what does it mean to have more the if dft frequencies that means that
0:07:11	um if if pulses finite length and you know there are certain approximations and there it really means
0:07:16	uh the dft F length of approximately the length of the pulse
0:07:20	more free is available means a longer part
0:07:23	so we we need to use either wider bandwidth or longer pulses
0:07:28	um
0:07:29	now
0:07:30	once we have that and have the matrix well you know it's a compressed sensing system
0:07:35	we all know we can use L zero minimization which we really can
0:07:38	uh we can use we can relax it the no one
0:07:41	minimization or we can use one of those ready out in score sound subspace space personal to all brown storm
0:07:48	all the M Ps that
0:07:50	exist in the field and we can recover the signal
0:07:53	now
0:07:55	i said before that pulse length and bandwidth term is
0:07:58	the number of degrees of freedom
0:08:00	so in general you would think that
0:08:02	the longer the pulse the better
0:08:04	and this is true
0:08:07	because you and the pulse to get shows make that gets reflected then you record it
0:08:11	but not always
0:08:12	so here's the case or we have a very long house
0:08:15	but the transmitter is the same as the receiver so what happens
0:08:19	we have a finite this but it time that paul street as the system and comes back
0:08:23	we still sending pulses and a receiver which is the same as a transmitter cannot switch modes and receive the
0:08:28	ball
0:08:29	so this is not this is not good
0:08:31	so we need to take into account the fact that there is a distance that were sensing and the pulses
0:08:36	can not be
0:08:37	longer than the round trip of that this
0:08:39	so this is something to think about
0:08:41	but
0:08:42	we can
0:08:43	but and that limits the number of degrees of freedom in the diverse we can introduce in the matrix
0:08:47	but of course there is a way out of it
0:08:49	which is due intermittent sing so intermittent pulsing so we send the small files
0:08:54	randomized
0:08:55	it comes we wait we receive it it comes back
0:08:57	then would send another poll cells are on the eyes different ball so that that
0:09:02	can help us in that particular situation
0:09:05	so
0:09:06	this is the system
0:09:08	a another question is that sometimes we have access to a very small physical array
0:09:13	so are are a my have very few elements it might not be sometimes they might be linear
0:09:18	um
0:09:18	we are not a it for example if the R is in there we're not gonna be able we we
0:09:23	have a fundamental but like up and down a big you in we're not gonna be able to
0:09:27	to reconstruct that sense
0:09:29	but that seen that we want to sense
0:09:31	uh in in that direction
0:09:33	um
0:09:34	even even if it's not
0:09:36	uh it's not there linear maybe this as are very close to each other and are not enough
0:09:40	um in in in a there's not enough separation to reconstruct things
0:09:44	and um
0:09:46	a and we don't have enough sensors to be able to have a that to very see
0:09:49	so what can we do to achieve
0:09:52	D reconstruction well this is a technique that
0:09:54	um has been used that lot for example synthetic aperture radar so on
0:09:58	we create a virtual a so we move the are a
0:10:01	at every point would also received data we keep moving it
0:10:05	and rate the virtual or synthetic are a if you want um which is well what we can do here
0:10:11	of course in this particular case if the
0:10:13	if the sensors are linear are there is always an up and down a but it which i'll get to
0:10:17	that in a minute
0:10:18	uh but for example if we
0:10:20	move the are a vertically
0:10:21	uh then there is no such thing the
0:10:24	the sensors are one i
0:10:26	a what does that mean that means we have
0:10:29	are one they one
0:10:30	for position one of the are a are two a two for position to of the a and so on
0:10:34	we can yet a big matrix
0:10:36	uh get the scene and and recovered using standard
0:10:39	group
0:10:42	now
0:10:43	oh
0:10:44	just realise
0:10:45	more time
0:10:46	um i'll get to the simulations uh we actually a simulated that system in uh in
0:10:51	uh our lab
0:10:53	um the the
0:10:54	system system that we chose to simulate is uh this particular sensor or it's a relatively wide band sensor the
0:11:00	centre frequencies forty heard
0:11:02	um you want to be on the relatively high frequency
0:11:06	uh for humans and dogs not be here in general
0:11:09	if you're doing that
0:11:10	uh the bandwidth is approximately ten to fifteen khz so it is a relatively wide band a
0:11:15	uh i i i are and wideband sensor this is the frequency response
0:11:19	um and the reconstruction of grin which was the users "'cause" sound when there is only just to do that
0:11:24	is that
0:11:25	if we have prior information
0:11:27	on the scene then we can use something like model based compressed sensing or something like that
0:11:31	and modify that reconstruction algorithm to be able to a help in the reconstruction from that scene
0:11:37	now these are
0:11:39	simulation results from a physical are a we had
0:11:41	um
0:11:42	five transmitters and three receivers
0:11:45	uh this is the scene we created
0:11:47	uh and this is distances in meters
0:11:50	um and this is of course the square we can slight structure without even thing any noise
0:11:55	as you can see least squares it's gone a result the scene there's not enough
0:11:59	uh
0:11:59	rank in the matrix to even produce anything
0:12:02	um if we use them processing in particular well as a said to use goes um
0:12:06	uh with three db S with thirty db snr by the way the colours here represent the reflectivity the the
0:12:12	intensity of the reflectivity of that particular scene
0:12:15	um we can get a pretty decent reconstruction
0:12:18	a pretty good construction of the same even with twenty db we get some artifacts but with can still get
0:12:23	some good reconstruction up to a almost a meter away from the a
0:12:29	um
0:12:30	uh here's another example of virtual array this is your it's seen i'm not saying uh you scores are constructions
0:12:35	kind of pointless
0:12:36	uh you could do it you just a noise
0:12:38	um here the is all seen um and the the the are is into positions now you might not is
0:12:45	that these are not exactly in there
0:12:47	there's slightly of said the middle elements of the array are slightly lower than the
0:12:51	than the outermost elements
0:12:53	and the reason is that we want to result this fundamental up and down um but so you want the
0:12:57	are rate to be not completely flat
0:12:59	a result that
0:13:00	uh this is the scene and this is what we can recover even with ten db signal-to-noise ratio which is
0:13:05	and these are meters
0:13:07	uh which is pretty a pretty bad
0:13:09	um
0:13:10	so
0:13:11	in conclusion um i'd like to make some remarks
0:13:14	so we didn't do would
0:13:16	where i think where the first that i've seen that we have all ultrasonic three D reconstruction using a single
0:13:21	or eight
0:13:22	um and what we exploit it is the near field properties is and and also
0:13:27	and compress size in of course but we also
0:13:30	um real exploit the fact that there is wide band
0:13:33	uh now i have to make a a a a point in that uh time and note here that
0:13:37	uh typically if you look for ultrasonic sensors
0:13:40	um there really keen to be narrowband uh i typical ultrasonic applications
0:13:45	i what people look for them is very narrow field of view and very in our band then the two
0:13:50	are compatible but in general
0:13:52	uh this is what people want which is completely opposite to what we want what what is nice
0:13:56	is that actually if you wanna make the are a wide band you also why don't the field of view
0:14:01	so this is if you want to make the sensor or then
0:14:04	a you know you why in the field of view which is really good for us
0:14:07	so there are there exist if you sense like the one i so
0:14:11	that
0:14:11	can have a band uh sense
0:14:14	now there are certain uh resolutions versus scene that trade offs
0:14:18	um generally the higher the frequency you can take the older sound
0:14:21	the better or there is a loose and you can get uh that has to do with a wavelet
0:14:25	with a wave length of the sound
0:14:28	um unfortunately one you're talking about over the air sensing
0:14:31	um
0:14:32	i frequency means that you can sense and like to centimetres in front of you not more
0:14:37	uh if you go like the five hundred khz or something
0:14:40	so that's for the khz is a pretty good uh that we use is a pretty good um
0:14:45	uh
0:14:47	frequency if you wanna do something and the or they're of uh a few meters up to i don't a
0:14:51	five six meters
0:14:53	um um there are some trade-offs uh in complexity versus performance so what that means
0:14:59	uh the number of um of trans uses we get
0:15:02	uh we can get better performance we have a that's or a we have a bigger matrix more
0:15:06	randomness this that we can introduce there
0:15:09	uh of course that means
0:15:10	a bigger cost for the E
0:15:12	um
0:15:13	a and more hardware complexity
0:15:15	what is interesting is that
0:15:18	if we increase the receivers
0:15:20	only
0:15:22	a than sorry the number of receiver is the only thing that um at as in terms of the computational
0:15:27	cost
0:15:28	the number of transmitters
0:15:29	really doesn't affect complexity that much except for creating that initial matrix
0:15:33	once you create that matrix a number of transmitters
0:15:36	uh um a not in the complex the length of the the system
0:15:40	a all you have to do with a with the receivers
0:15:42	which is good because in general up to up to a point we can increase transmitter an increase they've very
0:15:47	city without hurting or
0:15:49	are computational complexity
0:15:51	now
0:15:52	what uh this is a um
0:15:54	preliminary to
0:15:56	intermediate kind of work
0:15:58	um we are building a real system and are actually conducting experiments that
0:16:02	uh as we speak that have been is still very good results
0:16:05	uh there is some theoretical analysis that uh we need to do and
0:16:08	um that the difficulty in this analysis is that we're not talking about
0:16:12	an hour of frequencies were actually talking about wideband arrays and
0:16:16	oh there are some three key um
0:16:19	properties that we need to
0:16:20	yeah split there
0:16:21	so
0:16:22	with that i'm open to questions are common
0:16:36	um
0:16:37	since it's is is just an to motion or to sex i mean do you you to do do you
0:16:42	really "'em" is assumed it's been don't by a group of pose something uh and how how accurately do you
0:16:48	know the position of you move to write so this is something that uh we need to to examine um
0:16:53	i i expect to will be a bit sensitive that would like an know the most
0:16:57	a pretty well and and it's something that actually it's one of are our interest is not really the car
0:17:02	is that some mobile or so this is
0:17:04	kind of the next things that one of the next things that we really need to study
0:17:07	a sense to V R
0:17:08	i thing that um is important even with static is is how sense that we are to discrete a sum
0:17:13	of the space of course versus
0:17:15	fine
0:17:16	uh which is also another question that um
0:17:19	fine discretization position increases complex the by a lot
0:17:21	and it seems that uh we're pretty robust and uh there are ways even
0:17:26	even we should go to big extremes are ways that um
0:17:29	we can assess city
0:17:31	do of course is could a station and then zoom in the to the points of interest and the fine
0:17:35	this with basis
0:17:41	to talk wonder to show
0:17:44	we use of taking advantage of the structure
0:17:47	it was firstly
0:17:49	i to use for
0:17:50	for reconstruction of right this is one reason we use "'cause" sound
0:17:54	a there we can do a a a a very good the model based compressed sensing
0:17:58	i in which we can
0:17:59	we can look at nearby pixels we can look at the fact that
0:18:03	for example this is done that sparsity
0:18:05	but you know that um if you have a a an object there's nothing behind it so you can set
0:18:10	everything behind of to zero
0:18:11	uh you know things like that you can do uh we have a look at that and that in this
0:18:15	work but is definitely in all
0:18:21	a how was it different from a a system problem that we have
0:18:25	looking looking at of the people do which is actually
0:18:27	compressive sensing and don't to the real and compressive since is for the wheel the machine
0:18:33	and the that you
0:18:35	oh you are was much more
0:18:37	uh difficult issues with a text to the total did by at least the
0:18:41	is the more the result
0:18:43	oh
0:18:44	because of the two than interactions actions model the in section six plus
0:18:49	i have a a and in the target is frequency dependent as well i have seen that work at be
0:18:53	happy to say i does not how it is that you would you was wide band the use was to
0:18:57	speech and the frequency is and the three position C six is a simple okay well out that would be
0:19:03	happy to look at that work and uh
0:19:05	i at as we had the seem too much work can white but there is
0:19:08	uh
0:19:09	before
0:19:11	okay you
0:19:13	i

COMPRESSIVE SENSING FOR OVER-THE-AIR ULTRASOUND

Compressed Sensing and Sparse Representation of Signals

Presented by: Petros Boufounos, Author(s): Petros Boufounos, Mitsubishi Electric Research Laboratories, United States